Question

The choir sells tickets to its performances for an assortment of prices and gives some tickets away. The choir
director wants to look at the relationship between the number of seats occupied at each performance and the
ticket revenue for that performance. The data show a linear pattern with the summary statistics shown below:
mean
standard deviation
= number of seats occupied
= 75.8
8 = 14.8
y = ticket revenue (dollars)
Y = 696
Sy = 177.6
r= 0.81
Find the equation of the least-squares regression line for predicting the ticket revenue from the number of
seats occupied
Round your entries to the nearest hundredth.
y
HC

Answer 1

The least square regression equation for the information provided is y = 9.72x - 40.776

The general equation of a regression model can be expressed thus:

• y = bx + c

• Slope, b = r(Sy/Sx)

Calculating slope, b :

• b = 0.81(177.6 / 14.8) = 9.72

Plugging the values of b, y and x into the equation in other to calculate c :

696 = 9.72(75.8) + c

696 = 736.776 + c

c = 696 - 736.776

c = - 40.776

Therefore, the linear regression model can be expressed as : y = 9.72x - 40.776

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